Question REgarding Reimann integral

[shehpar]

Let g:[0,1]--[0,1] be defined by g(x)=1 for x belongs to (0,1] and g(0)=0. Prove that g belongs to R[0,1]?
and evaluate integral of g with lower limit 0 and upper limit 1.. I will really appreciate the ansawer. thanks

 

[slider142]

This question belongs in the undergraduate coursework section of this site. Also, please see https://www.physicsforums.com/showthread.php?t=94383 on posting guidelines when requesting coursework help.

 

[shehpar]

But where to find undergraduate section. I couldn't find. would you please tell me where is that section. thanks

 

[snipez90]

It's more important that you show some work. I'll get you started. What is simple but effective partition to choose here? Assuming you understand the basic definitions involved, including what upper and lower sums are, this problem really comes down to understanding how to deal with the point of discontinuity by choosing the right partition.

 

[shehpar]

Thanks for reply,I am sure that point of discontinuity is zero here and, I know about upper and lower sum .. I don't know how to choose the right partitions. I wish, I could.. In fact, I really don't know how to prove that something is Remiann integrable